The following is a list of definitions of many of the concepts and statistics found throughout Advanced Football Analytics.

Air Yards (AY) - The passing yards forward of the line of scrimmage in which the ball travels through the air. In other words, it is total passing yards minus any yards after catch (YAC) gained by the receiver.

Air Yards Per Attempt (Air YPA) - The average air yards (AY) gained per pass attempt. Note that this does not include any sack yards.

Win Probability (WP) – The probability that a team will win a game in progress, given a particular combination of circumstances including score, time remaining, field position, down, and to go distance. WP is based on a model built on actual outcomes of NFL games from recent seasons that featured similar circumstances.

Win Probability Added (WPA) – The difference between a team’s Win Probability (WP) at the start of a play and the WP at the end of the play. WPA is the measure of a play’s impact on the outcome of a game. An individual player’s WPA is the sum of the WPA of the plays in which that player was directly involved. Being directly involved is defined as an offensive player who ran, threw, or kicked the ball, was targeted by a pass, or flagged for a penalty. Defensive players are credited for WPA when they tackle or sack the ball carrier, are credited with an assisted tackle or sack, cause a fumble, defend a pass, or are flagged for a penalty. Expected Points (EP) – The value of the current down, distance, and field position situation in terms of future expected net point advantage. In other words, it is the net point value a team can expect given a particular combination of down, distance, and field position. First and goal at the one represents an EP near 6, while 3rd and 20 at a team’s own one yard line represents an EP of about -2. EP differs from Win Probability (WP) in that it does not take into account the game score and time remaining.

Expected Points Added (EPA) – The difference between the Expected Points (EP) at the start of a play and the EP at the end of they play. EPA is the measure of a play’s impact on the score of the game. An individual player’s EPA is the sum of the EPA of the plays in which that player was directly involved. Being directly involved is defined as an offensive player who ran, threw, or kicked the ball, was targeted by a pass, or flagged for a penalty.

Win Probability Added per Play (WPA/P) – The average Win Probability Added per play in which an offensive player is directly involved. WPA/P is a measure of an individual player’s impact on the outcome of his games, on a per play basis.

First Down Probability (P(1D)) – The probability that the offense will earn a new series of downs (or score a TD if it's goal-to-go) based on the current down and distance.

Expected Points Added per Play (EPA/P) – The average Expected Points Added per play in which an offensive player is directly involved. EPA/P is a measure of an individual player’s impact on the scores of his games, on a per play basis. EPA/P differs from WPA/P in that it is not as context-sensitive because it does not consider game score and time remaining.

Positive Win Probability Added (+WPA) – The Win Probability Added attributed to a defensive player, limited to only the plays that are net positives for his team. It is a measure of a defender’s impact on the outcome of games in terms of play-making ability. Only positive plays are considered for individual defenders because very good individual plays can still result in net losses in WPA. For example, a safety who makes a shoe-string tackle to stop a TD would be a great individual play, but the play as a whole would still be a net negative outcome for his team. However, overall individual WPA likely correlates well with +WPA.

Positive Expected Points Added (+EPA) -- The Expected Points Added attributed to a defensive player, limited to only the plays that are net positives for his team. It is a measure of a defender’s impact on the game score in terms of play-making ability. Like for +WPA, only positive plays are considered for individual defenders because very good individual defensive plays can still result in net losses in EPA. However, overall individual EPA likely correlates well with +EPA.

Positive Win Probability Added per Game (+WPA/G) – The measure of a defender’s impact on the outcome of his team’s games, on a per-game basis. Like +WPA, +WPA/G is limited to positive plays for individual defensive players.

Positive Expected Points Added per Game (+EPA/G) – The measure of a defender’s impact on the outcome of his team’s games on a per-game basis. Like +EPA, +EPA/G is limited to positive plays for individual players.

Tackle Factor (TF) – The ratio of a player’s proportion of his team’s tackles compared to what is expected at his position. For example, middle linebackers in a 4-3 typically make 11.9% of their team's tackles. A MLB who made 12.6% of his team's tackles would have a TF of 11.9/12.6 = 1.06. TF is adjusted for a full 16-game season.

Success Rate (SR) – The proportion of plays in which a player was directly involved that would typically be considered successful. Specifically, SR is the percentage of plays resulting in positive Expected Points Added (EPA).

Success Count (SC) – The number of plays in which a player was directly involved that would typically be considered successful. Specifically, SC is the number of plays resulting in positive Expected Points Added (EPA). SC is used primarily for individual defenders, because they should not be penalized for making tackles even if the offense has improved it's EP.

Yards per Attempt (YPA) – Yards gained per pass attempt.

Adjusted Yards per Attempt (AYPA) – A quarterback’s Yards per Attempt (YPA) minus sack yards, adjusted by a 45-yard penalty for each interception thrown. 45 yards is chosen because it is approximately equivalent to the Expected Point (EP) value of an interception.

Deep Pass Percentage (Deep%) – The proportion of pass targets in which a receiver is greater than 15 yards beyond the line of scrimmage.

Quarterback Hits (QBHits) – The number of times a defender is able to hit the quarterback who is in the process of throwing the ball or immediately following a throw.

Passes Defended (PD) – The number of passes successfully deflected by a defender.

Excitement Index (EI) – The measure of how exciting a game is. EI measures the total movement of the Win Probability (WP) line during a game. The more that WP fluctuates, the more dramatic, uncertain, and exciting a game is.

Comeback Factor (CBF) – The measure of how big a comeback is in a game. CBF is defined as the inverse of the winning team’s lowest Win Probability (WP) during a game. For example, if a winning team’s lowest point in a game is 0.10 WP, its CBF would be 10, which is 1 / 0.10. The higher the CBF, the bigger the comeback.

Leverage Index (LI) – The measure of how critical a play is in potentially determining the outcome of a game. Specifically, LI is based on the difference between the Win Probability Added (WPA) of a potential “good” outcome and the WPA of a “bad” outcome. The LI is the ratio of the potential good WPA to an NFL-average typical WPA.Plays in the final minutes of a close game will have very high LIs, while plays toward the end of blowout games will have very low LIs.

Generic Win Probability (GWP) – The probability that a team would win a game against a notional league-average opponent at a neutral site. GWP is based on actual NFL game outcomes from recent seasons. GWP considers each team’s offensive and defensive running and passing efficiency, turnover rates, and penalty rates, weighted according to how predictive each stat is in determining winners. Adjusted GWP (AdjGWP) is corrected for the strength of a team’s past opponents.

Offensive Generic Win Probability (OGWP) – The probability that a team would win a game against a notional league-average opponent at neutral site, assuming the team in question had a league-average defense. Adjusted OGWP (AdjOGWP) is corrected for the strength of a team’s past opponent defenses.

Defensive Generic Win Probability (DGWP) – The probability that a team would win a game against a notional league-average opponent at neutral site, assuming the team in question had a league-average offense. Adjusted DGWP (AdjDGWP) is corrected for the strength of a team’s past opponent offenses.

Yards After Catch (YAC) - The yards gained by a receiver after catching a pass.

what explains the fact that a teams total # of passing yards does not equal the total amount of all individual passers....basically, when does a team not get credit for passing yards even though the player does???

1. For defensive backs, do you have QB rating against stat? The one stat for DBs that is always missing is how many times they were thrown at. 2. Does your adjusted QB rating also take into account drops?

I notice that a player can have a positive Win Probability Added but a negative Expected Points Added (for example, Running Back Tim Hightower in his first game of the 2011 season). How does this happen? I would imagine that contributing negative points should not increase probability of a win. Is it just error in the models that allows this to happen or is there something more systematic that explains this?

David-It happens all the time. Say there is a player who plays marginally below avg all game and has negative EPA. But at the end of a close game he converts a critical 3rd down, keeping a potentially game-winning drive alive. He would have positive WPA and negative EPA.

Also, there are plays that could have negative EPA but positive WPA simultaneously. WPA says that taking a sack is better for a team with a lead than completing a 5-yd pass in which the receiver runs out of bounds and stops the clock. The sack would have pos WPA but neg EPA. The pass would have neg WPA but pos EPA.

Ok, turns out I'm still confused (ok if you don't have the time to un-confuse me). In your exampleof positive WPA co-occurring with negative EPA, a QB taking a sack is better than a 5-yard completion precisely because the former predicts a lower probability of additional points for the opposing team than the latter. So I would think that WPA and EPA should go hand-in-hand here. I guess I was viewing EPA as a 'net' statistic, i.e., predicting net-points added (player's team points minus opposing team's points). But I guess EPA is only focused on the player's team, and doesn't take into account the effect of a play on the opposing team's probability of additional points.

David, I think the thing you are missing is the time component of WPA. The point is towards the end of the game, a running clock is more valuable to the team ahead than a few yards, or more likelihood of scoring more points (in some instances)

thanks Chris, I understand your point that a running clock is more valuable than a few yards or the likelihood of the winning team scoring, but this is because a running clock reduces the other team's chances of scoring points. I thought the EPA statistic was a 'net points' statistic, and therefore would reflect something that lowers the other team's chances of scoring. But it sounds like EPA focuses only on one team at a time, and does not take into account time in the game (so a 50 yard pass to the 1-yard line as time expires would actually increase EPA).david

What stat can you use to compare defensive players with offensive? WPA and +WPA? For example, Tom Brady has 2011 WPA of ~7.5 and Derrelle Revis has +WPA of +1.8. Are these two numbers comparable. Is Brady ~4X more valuable than Revis? If not how would you make the comparison?

No. Sorry, that's not comparable. +WPA only counts the "good" side of WPA. We could compare Revis' +WPA with Brady's +WPA instead of his total WPA, but I think the qualitative difference between their positions limits the meaning of the comparison.

Is there any way to determine how many times a certain D-lineman is double teamed? Like for example on offense, how many plays Jimmy Grahm made plays against double team. I am mostly interested on the defensive side on the line. (individuals doubled by O-line men)

How come the Redskins have the biggest rushing EPA but one of the worst Rushing WPA, and in fact are rated as the third worst offensive line, with Alfred Morris listed at 16th in the running back stats. Something doesn't feel right here, but am I misreading something?

On the Advanced Team Stats page, it shows that NE has an OffWPA of 5.81. Am I correct in thinking that that is the total WPA sum of all of New England's offensive plays? Is it correct to say that each football situation has a WP, and each play then has a resultant WPA? Thanks!

Are sacks factored into QB hits, or are they considered 2 separate events? So for example if a QB has 50 hits and 20 sacks, that would be 70 times somebody got into the backfield and made a play on the QB.

@BBurkeESPN

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